Shell Method

Shell Method

Shell Method is particularly good for calculating volume of a 3D shape by rotating a 2D shape around a VERTICAL LINE.Imagine there is a CYLINDER, and we’re to calculate the surface area of the cylinder, and integrate the surface areas when the cylinder gets thiner and thiner.

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Refer to Khan academy: Shell method for rotating around vertical line?Jump to Khan academy for some practice: Shell method?Refer to Desmos Animation: Solids of Revolution (about y-axis)

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?Refer to the awesome article: The shell method of finding volumes of revolution

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?Refer to mathdemos.org for more intuitive animations: SHELL METHOD DEMO GALLERY

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Example

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Solve:

  • Let?s draw it out first:

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  • Based on the Shell method of integrating Cylinder’s shells, we got the equation:

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